Question

1. If a, b, c, d, and e are whole numbers and a(b(c

+ d) + e) is odd, then which of the following
CANNOT be even?
(A) a
(B) b
(C)c
(D) d

Answer 1

a CANNOT be even ⇒ answer A

Explanation:

* Lets revise the rules of even and odd numbers

- Even numbers any number its unit digit is (0 , 2 , 4 , 6 , 8)

- Odd numbers any number its unit digit is (1 , 3 , 5 , 7 , 9)

# even + even = even ⇒ 2 + 4 = 6

# odd + odd = even ⇒ 1 + 3 = 4

# odd + even = odd ⇒ 1 + 2 = 3

# even × even = even ⇒ 2 × 4 = 8

# odd × odd = odd

⇒ 3 × 5 = 15

# odd × even = even ⇒ 5 × 6 = 30

∵ a[b(c + d) + e] = odd

∵ odd × odd = odd

∴ a must be odd and [b(c + d) + e] must be odd

∵ odd + even = odd

∵ odd × even = even

# Case 1

∴ b(c + d) must be odd if e even

∵ b(c + d) is odd

∴ b must be odd and (c + d) must be odd

∵ c + d must be odd

∵ odd + even = odd

∴ c or d can be even

- We now now that e , c and d can be even

# case 2

∴ b(c + d) must be even if e odd

∵ b(c + d) is even

∵ even × even = even

∴ b and (c + d) both can be even

∵ c + d can be even

∴ c or d can be even or odd

- We now now that e , c , d and b can be even

∴ Only a can not be even

* a CANNOT be even